Let $q : S^{2n+1} → CP^n$ be the usual quotient map. Is $q$ a covering space?

Question

Let $q : S^{2n+1} → CP^n$ be the usual quotient map. Is $q$ a covering space ?

I only know the definitions. But how to do this one? Any ideas please.

Answer 1

It is not a covering, because both spaces do not have the same dimension. But you have a fibration $S^1\rightarrow S^{2n+1}\rightarrow CP^n$.

https://en.wikipedia.org/wiki/Complex_projective_space#Topology